Cone beam (CB) computed tomography (CT) involves the imaging of the internal structure of an object by collecting several projection images (“radiographic projections”) in a single scan operation (“scan”), and is widely used in the medical field to view the internal structure of selected portions of the human body as well as in the industrial and security fields to perform non-destructive inspection and to detect contraband and weapons in security screening. Typically, several two-dimensional projections (which are images) are made of the object, and a three-dimensional representation of the object is constructed from these projections using various tomographic reconstruction methods. From the three-dimensional data sets, conventional CT slice images through the object can be generated. The two-dimensional projections are typically created by transmitting radiation from a “point source” through the object, which will absorb some of the radiation based on its size and density, and collecting the non-absorbed radiation onto a two-dimensional imaging device, or imager, which comprises an array of pixel detectors (simply called “pixels”). Such a system is shown in FIG. 1. Typically, the point source and the center of the two-dimensional imager lie on a common axis, which may be called the projection axis. The source's radiation emanates toward the imaging device in a volume of space approximately defined by a right-circular cone, with roughly circular- or ellipse-shaped cross sections perpendicular to the axis (where deviations are caused by non-ideal aspects that include the heel effect in X-ray sources), having its vertex at the point source and its base at the imaging device. This is the reason the radiation is often called cone-beam (CB) radiation. The imagers in state-of-the-art CBCT systems measure around 30 cm by 40 cm, having approximately 750 rows of pixels with approximately 1,000 pixels in each row, for approximately 750,000 pixels. Generally, when no object is present within the cone, the distribution of radiation is substantially uniform on any roughly circular or elliptical area on the imager that is centered about the projection axis, and that is within the cone. However, the shape of the radiation boundary on the imager may be non-uniform, from a large number of perturbations, so that there is no perfect rotational symmetry about the projection axis. In any event, any non-uniformity in the distribution can be measured in a calibration step and accounted for. The projection axis may not be at the center of the imager or the center of the object. It may pass through them at arbitrary locations including very near the edge.
In an ideal imaging system, rays of radiation travel along respective straight-line transmission paths from the source, through the object, and then to respective pixel detectors without generating scattered rays. However, in real systems, when photons of X-radiation in rays interact with a portion of the object (including photoelectric, Compton and pair production interactions), one or more scattered rays are often generated that deviate from the transmission path of the incident radiation. These scattered rays are often received by “surrounding” pixel detectors that are not located on the transmission path that the initial photon-containing-rays of radiation was transmitted on, thereby creating errors in the electrical signals of the surrounding pixel detectors. Also, in typical two-dimensional imagers, the radiation meant to be received by a pixel is often scattered by various components of the source-imager system (e.g., scintillation plate, bow tie filters, radiation hardening filters, the metal anode that electrons hit in the source to produce X-rays etc.), and received by surrounding pixels. These effects are often characterized, in part, by a point-spread function (PSF), which is a two-dimensional mapping of the amount of error caused in surrounding pixels by a given amount of radiation intended for a central pixel. The surface of the PSF is similar to the flared shape of a trumpet output, with the greatest amount of error occurring in pixels adjacent to the central pixel.
Each of the above non-ideal effects creates spatial errors in the pixel data generated by the two-dimensional imager. In turn, the spatial errors cause artifacts (e.g., phantom images) and loss of resolution and contrast and blurring in the CBCT image slices produced by the radiation imaging system.